Cryptographic systems are used in the communications industries in applications that require some level of security. The need for security arises from the requirement that only the sender and receiver be privy to the information contained in the communications between them. Typically, a cryptographic system is employed in such a way that the sender encrypts the data before it is sent, and the receiver decrypts the data upon receiving it. The data should be encrypted in such a way that a third party cannot interpret it into a useful form if its intercepted during transmission from the sender to receiver.
Typical cryptographic systems are based on the concept of defining a mathematical function that maps the data to the encrypted form. After mapping the data using such a function, the sender transmits the encrypted data. After the encrypted data is received, the inverse of the mathematical function is applied to convert the data back into easily understood form. Typically, the sender and receiver keep secret between themselves some property of the function, called the key, so that a third party would not be able to intercept and decrypt the data without authorization. For example, the coefficients of the equation that is used to encrypt the data would be kept secret.
Examples of the types of data that require cryptographic methods are related to national security, corporate financial assets, and plans for corporate product releases. Typical practitioners of cryptographic methods include national governments, corporations, and financial institutions. These organizations typically protect data such as plain text documents, e-mail, and financial spreadsheets, any of which may be detrimental if enemies of the state or corporate competitors would pirate the information.
In the field of photography, there is a growing need to transmit digital images securely. Digital images are created by either scanning pictures from photographic film or prints, or directly from digital cameras. Professional photographers consider their images to be assets that must be protected from theft, or else financial loss would result. As a result, the digital images are typically in the form of computer files, and the protection must be of the form that prevents pirates from using those files in a meaningful or commercial way.
There is a particular need in the field of cinematography for protecting digital images from piracy. The major studios that produce motion picture movies for cinema have publicly stated their intent to convert from optical projection systems to digital projection systems. The cinema industry will convert from the existing distribution system, which is based on distributing movies on photographic print film, to a system based on the distribution of movies in digitized form. Their concern over security of their movies, in turn, converts from preventing the burglary of the optical prints to preventing the piracy of digital image computer files.
To date, the only security system for digital cinema is the application of cryptographic methods. The digital form of the movie would be encrypted by the studio that owns it. In the encrypted form, the digital movies would be unintelligible, so that the digital movie would be useless to a third party who pirates it. The movies would be transmitted by satellite, or any other suitable medium, to the theater for projection. At the time of projection, the digital movie would be decrypted.
Ideally, the digital movies would be decrypted in “real-time,” that is, as the movie is being projected. This places great demands on the cryptographic algorithm. In digital cinema the images would have to be decrypted at 24 images per second if real-time decryption was desired. The minimum size for digital cinema images are 2000×3000 pixels, or 6,000,000 pixels overall. Each pixel comprises three values, one each for red, green, and blue components of the image. Each of these values must be at least 8 bits. The result is that, for real-time cryptographic applications of digital cinema, at least 3.4 gigabits must be decrypted per second.
Currently, classical encryption techniques are being applied to the problem, but they are inadequate for two reasons. First, they are not fast enough for real-time decryption on a frame-by-frame basis. Consequently in many applications, frames are only partially encrypted leaving some of the movie vulnerable for piracy. Also, the frames are only encrypted with an insufficient level of security that allows faster encryption and decryption techniques. But, again, the digital movie is vulnerable for piracy. Second, the classical techniques are limited by hardware storage capacities requiring huge buffering capacity and complex software to manage the input/output of the images.
Elliptical curves have recently been applied in cryptographic solutions. While great strides have been made in their implementation, they are still too slow for digital cinema applications. In their optimum efficiency, quadratic and trinomial equations must be solved for each block of data that is encrypted, resulting in large amounts of computation time.